JEE Advanced 2023 — Paper 2 — Question 41

A cylindrical furnace has height $(\mathrm{H})$ and diameter (D) both 1 m . It is maintained at temperature 360 K . The air gets heated inside the furnace at constant pressure $P_{\alpha}$ and its temperature becomes $T=360 \mathrm{~K}$. The hot air with density $\rho$ rises up a vertical chimney of diameter $\mathrm{d}=0.1 \mathrm{~m}$ and height $\mathrm{h}=9 \mathrm{~m}$ above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density $\rho_{\alpha}=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$, pressure $\mathrm{P}_{\alpha}$ and temperature $\mathrm{T}_{\alpha}=300 \mathrm{~K}$ enters the furnace. Assume air as an ideal gas, neglect the variations in $\rho$ and T inside the chimney and the furnace. Also ignore the viscous effects. [Given: The acceleration due to gravity $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$ and $\pi=3.14$ ]

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is $\_\_\_\_$ $\mathrm{gm} \mathrm{s}^{-1}$.